Yes, no issue at all. Simply backup the current iPad with iTunes and then connect the new iPad and iTunes will prompt you to either restore the backup or set up as a new iPad. Select restore and all your apps and settings (but not passwords) will be applied to the new iPad.
Yes, you can wipe the old one. In iTunes, once connected, select the device in the left hand column and there will be an option to reload the OS effectively wiping all your apps.
Don't bother with a computer installed iTunes program for backup, its obsolete.
iCloud doesn't back up music and video you might have sync'd with the iPad. Also if you back up using iTunes and turn on the password option - the backup will save passwords for email accounts and WiFi networks. iCloud doesn't.
I know as a friend of mine had his iPhone replaced and the iCloud backup was only some of the stuff he had on his phone.
Jamesbe* pro (16.8 / 1.2 sync) - BQM - FTTC cab installed 18-jun-2012 - not yet active - est 44.6 / 6.5
Sat 21-Jul-12 11:38:25